In a large pot, heat the olive oil over medium heat. Add the chicken breast, onion, and poblano pepper. Cook, stirring frequently, until the chicken breast chunks are browned on all sides, about 7-8 minutes.
Add the salt, pepper, chili powder, cumin, and garlic. Cook for another 1 minute, stirring well.
Add the green chiles and chicken broth to the pot. Bring to a boil, then reduce to a simmer. Let cook uncovered for 10 minutes.
Add the cream cheese and cook, stirring often, until all the cream cheese melts into the broth, about 4-5 minutes. Stir in the heavy cream and remove the pot from the heat.
Taste the chili and adjust the seasonings to your liking. If it's too thin, you can return the pot to a low simmer for a few minutes, stirring occasionally, to thicken it. Let the chili rest off heat for 5 minutes to allow the flavors to meld.
Serve hot, garnished with chopped cilantro, if desired.